Automobile
license plate numbers are created using letters and digits.
State governments decide upon the specific arrangement of letters
and numbers that will be used for each state. It is important
to choose wisely on the pattern of possible numbers and letters,
since the possible number of combinations will determine the number
of cars that can be registered at any one time.

1. Complete the
chart below showing how many combinations are possible (that is, how many
cars can be registered) based upon the license plate arrangement schemes
developed by each state.

State

License Arrangement Scheme

Number of Registered Cars

1

6 characters in the plate
with three letters followed by three numbers

2

6 characters in the plate
with three letters (not the letter O) followed by three
numbers OR three numbers followed by three letters (not
the letter O).

3

5 characters in the plate
being either a letter or a number.

4

4 characters in the plate
being only letters.

5

4 characters in the plate
with one letter followed by 3 numbers.

2. A
witness observes a motorist leaving the scene of a crime in State #1
(appearing in the chart above). The witness remembers that the
first three letters of the license plate on the get-away car were
the letters UGG. How many license numbers in this state start
with these three letters?

3. The
city in which the crime discussed in question 2 occurred, represents
approximately 5% of the state's total population. How many
cars from this city would fit the get-away car's description?

4. Upon
further reflection, the witness remembers that the car was a
convertible with the top up. If the state records show that
only 12% of the state's registered cars are convertibles, how many
state wide cars are suspect? How many city cars are suspect?

5. In
State #3 (appearing in the chart above), a driver wants his license
plate to begin with the letters BOB. How many combinations are
possible that start with BOB?

6. In
State #5 (appearing in the chart above), a driver wants her license
plate to end with the her house number, 374. How many
combinations are possible that end with 374?